Optical scanning lens, optical scanning device and image forming apparatus

ABSTRACT

An optical scanning lens used in a scanning and imaging optical system in which a beam deflected by a light deflector is condensed on or in the vicinity of a surface to be scanned. The optical scanning lens is formed through plastic mold, and a distribution of the refractive indexes Δn(x) inside of the optical scanning lens has a local maximum within a range through which the beam passes through the lens.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No.10/315,183, filed Dec. 10, 2002, now U.S. Pat. No. 7,130,130, which is acontinuation of U.S. application Ser. No. 09/865,523, filed May 29,2001, now U.S. Pat. No. 6,532,094, issued Mar. 11, 2003, and is basedupon and claims the benefits of priority from the prior Japanese PatentApplication No. 2000-161586, filed on May 31, 2000, all of which arehereby incorporated by reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an optical scanning lens, an opticalscanning device and an image forming apparatus.

2. Description of the Related Art

In an optical scanning device widely known with reference to a laserprinter, a digital copier, and so forth, a beam emitted from a lightsource is deflected by a light deflector, the deflected beam iscondensed toward a surface to be scanned by a scanning and imagingoptical system, a beam spot is formed thereby on the surface to bescanned, and thus, optical scanning of the surface to be scanned isperformed.

Recently, a plastic-made (made of plastic) optical scanning lens isemployed as the scanning and imaging optical system or as a partthereof.

The plastic-made optical scanning lens is formed through plastic mold.As this type of lens can be easily mass-produced, it can be manufacturedat low costs. Accordingly, by employing the plastic-made opticalscanning lens, it is possible to effectively reduce the costs of thescanning and imaging optical system, and, thereby, the costs of theoptical scanning device. Further, with regard to the plastic-madeoptical scanning lens, it is possible to easily form a special lenssurface shape such as an aspherical surface through plastic mold.Accordingly, it is possible to simplify the scanning and imaging opticalsystem (reducing the number of lenses required) and/or to improveoptical performance thereof.

However, this type of plastic-made optical scanning lens has a problemin that a non-uniform distribution of the refractive indexes occursinside of the plastic-made optical scanning lens.

Through plastic mold, molding is performed in which thermally moltenplastic material is injected into a die, and is cooled in the die. Atthis time, cooling begins from a part of the material in contact withthe die. Accordingly, the center of the plastic material is cooledslowly relative to the periphery thereof. Thereby, a non-uniformdistribution of density (the density at a part cooled rapidly becomeshigher than that at a part cooled slowly) inside of the plastic. As aresult, the distribution of the refractive indexes of the thus-formedlens is not uniform inside thereof. As the density of the periphery ofthe formed lens is higher than that of the center thereof, therefractive index is lower at the lens center while, the nearer to thesurface the position thereof becomes, the higher the refractive index ofthe formed lens becomes, in general.

When the distribution of the refractive indexes of the plastic lens ismeasured by a method described later, the variation in refractive indexis like an approximately quadratic curve along each of a lens opticalaxis direction, a main scanning direction and a sub-scanning direction.

The plastic-made optical scanning lens is designed assuming that thedistribution of refractive indexes inside thereof is uniform.Accordingly, when the plastic lens has a non-uniform distribution ofrefractive indexes inside thereof, it cannot exhibit the performanceaccording to the design. Specifically, defocus occurs such that aposition of imaging of the deflected beam differs from the surface to bescanned, thereby, a position of beam waist of the deflected beam ischanged from the surface to be scanned, and, as a result, the diameterof the beam spot increases.

In order to reduce such a non-uniform distribution of refractive indexesinside of the lens, it can be considered to cool the molten plasticmaterial in the die, very slowly for a long time (for example, for tenand some hours) in a thermostatic chamber. However, by such a method,the productivity of the optical scanning lens becomes worse, and themanufacturing costs thereof increase. Accordingly, the advantage of theplastic-made lens such as requiring low costs may be cancelled.

SUMMARY OF THE INVENTION

An object of the present invention is to provide an optical scanninglens which has a no problem in optical performance/characteristicsthereof, even having relatively a large distribution of refractiveindexes inside thereof.

An optical scanning lens according to the present invention is anoptical scanning lens used in a scanning and imaging optical system forconverging a beam deflected by a light deflector onto or in the vicinityof a surface to be scanned, and is formed through plastic mold, and, adistribution of refractive indexes Δn(x) inside of the lens has a localmaximum, within a range through which the beam passes through the lens.

The above-mentioned scanning and imaging optical system may include onlya single lens, or a plurality of lenses, or at least one lens and amirror surface (concave surface/convex surface) having an imagingfunction.

The optical scanning lens according to the present invention is used asat least a component of the scanning and imaging optical system, and,one or a plurality thereof is/are disposed in the scanning and imagingoptical system. It is also possible that the scanning and imagingoptical system is formed by the optical scanning lens itself.

As a plastic material of the optical scanning lens, any one of acrylicresin (PMMA/alicyclic acrylic resin), PC (polycarbonate), polyolefinresin (ordinary polyolefin/alicyclic polyolefin), and so forth can beused.

When a lens is formed through plastic mold by using such resin material,acrylic resin has an advantage such that the optical elastic constantthereof is small and double refraction is not likely to occur therein.PC has an advantage such that the refractive index thereof is high,also, the moisture absorbing rate thereof is small, and, the opticalcharacteristics of the lens is not likely to be affected by theenvironment. Polyolefin resin has an advantage such that the moistureabsorbing rate thereof is small, and double refraction is not likely tooccur therein.

Any of the above-mentioned materials causes a non-uniform distributionof refractive indexes inside the lens during a process of the plasticmold therefor. Thereamong, polyolefin resin is one which causes anon-uniform distribution of refractive indexes during the process of theplastic mold, most remarkably. Therefore, the present invention iseffective in a case where the polyolefin resin is used as a material ofthe optical scanning lens.

The above-mentioned range through which the beam passes through the lensis a range for which the beam deflected by the light deflector passesthrough the lens during the deflection thereof. Specifically, withrespect to the main scanning direction, this range is a range throughwhich the deflected beam passes through the lens so that the beam thushaving passed through the lens scans an effective writing range on thesurface to be scanned. With respect to the sub-scanning direction, therange through which the beam passes through the lens is a rangedetermined in consideration of a possible variation in angle of emissionof light from the light source, a possible inclination of the deflectionreflective surface of the light deflector, and so forth. The rangethrough which the beam passes through the lens with respect to thesub-scanning direction may be preferably ±2 mm from a plane parallel tothe main scanning direction and including the optical axis, normally, inthe scanning and imaging optical system of a laser printer or the like.The size of the range through which the beam passes through the lens mayvary according to optical requirements such as the effective writingrange, diameter of beam spot, and so forth.

The definition of the above-mentioned distribution of the refractiveindexes Δn(x) inside of the lens will be described later.

The above-mentioned feature of the present invention in that thedistribution of the refractive indexes Δn(x) has a local maximum meansthat, when this distribution is approximated by using a polynominal, ofan order equal to or more than third order (practically, even order, notless than fourth order and not more than tenth order), of a variable x,within the range through which the beam passes through the lens, thethus-approximated distribution has a range in which dn/dx=0 and alsod²n/dx²<0, hereinafter.

It is preferable that the above-mentioned distribution of the refractiveindexes Δn(x) also has a local minimum. This means that theabove-mentioned approximated distribution also has a range in whichdn/dx=0 and also d²n/dx²>0, hereinafter.

Further, it is preferable that the above-mentioned distribution of therefractive indexes Δn(x) satisfies the following requirement:0.1×10⁻⁵ <LMAX[Δn(x)]−min[Δn(x)]<4×10⁻⁵  (1)where LMAX[Δn(x)] denotes the above-mentioned local maximum, andmin[Δn(x)] denotes the minimum value of the above-mentioned distributionof the refractive indexes Δn(x).

Further, it is preferable that the above-mentioned distribution of therefractive indexes Δn(x) satisfies the following requirement:1≦{max[Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]}<15  (2)where max[Δn(x)] denotes the maximum value of the above-mentioneddistribution of the refractive indexes Δn(x).

Furthermore, it is preferable that the above-mentioned distribution ofthe refractive indexes Δn(x) is a distribution in a sub-scanning sectionon or in the vicinity of the center of the lens in the main scanningdirection.

The above-mentioned sub-scanning section means an imaginary planarsection of the optical scanning lens perpendicular to the main scanningdirection. Similarly, a planar section parallel to the main scanningdirection and including the optical axis is called a ‘main scanningsection’.

It is also preferable that the above-mentioned distribution of therefractive indexes Δn(x) satisfies the following requirements same asthe above-mentioned requirements (1) and (2):0.1×10⁻⁵ <LMAX[Δn(x)]−min[Δn(x)]<4×10⁻⁵  (1)1≦{max[Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]}<15  (2)

The optical scanning device according to the present invention deflectsthe beam coming from the light source at a uniform angular velocity bythe light deflector having the deflection reflective surface, condensesthe deflected beam on the surface to be scanned as a beam spot by thescanning and imaging optical system, and, thus, performs opticalscanning of the surface to be scanned at a uniform velocity.

As the light source, any one of various types of solid lasers, gaslasers, LEDs, and so forth may be used. However, a semiconductor laseris most preferable. The above-mentioned surface to be scanned issubstantially, a photosensitive surface of a photosensitive medium (forexample, a photoconductive photosensitive body).

In the above-mentioned optical scanning device, the above-mentionedoptical scanning lens according to the present invention is used atleast as a part of the scanning and imaging optical system.

An image forming apparatus according to the present invention performsoptical scanning of the surface to be scanned so as to form a latentimage thereon, and visualizes the latent image so as to obtain a printedimage. In the image forming apparatus, as the optical scanning devicefor performing the optical scanning of the photosensitive surface of thephotosensitive medium, the above-mentioned optical scanning deviceaccording to the present invention is used.

The photosensitive medium may comprise a photoconductive photosensitivebody, and the electrostatic latent image formed on the photosensitivesurface through uniform changing and optical scanning of thephotosensitive surface may be visualized into a toner image. The tonerimage is fixed onto a sheet-like recording medium (such as a transferpaper sheet, an OHP sheet (plastic sheet used for an overheadprojector), or the like). In such a case, the image forming apparatus isembodied as a laser printer, a laser plotter, a digital copier, afacsimile machine, or the like

However, as the above-mentioned photosensitive medium, for example, asliver bromide photographic film may be used. In this case, the latentimage formed through optical scanning by the optical scanning device canbe visualized through an ordinary silver bromide photographic process.In such a case, the image forming apparatus is embodied as an opticalplate making apparatus, an optical drawing apparatus or the like.

Thus, according to the present invention, the optical scanning lens canhave optical characteristics, occurs practically no problems even havinga remarkably non-uniform distribution of refractive indexes insidethereof. Accordingly, by using the image forming apparatus including theoptical scanning device employing this optical scanning lens, it ispossible to render a satisfactory image formation.

Other objects and further features of the present invention will becomemore apparent from the following detailed description when read inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an optical scanning device in one embodiment of thepresent invention;

FIGS. 2A through 2E illustrate a distribution of refractive indexesinside of an optical scanning lens;

FIG. 3 illustrates an influence of a non-uniform distribution ofrefractive indexes inside of a lens to optical characteristics of thelens;

FIG. 4 illustrates increase in diameter of beam spot occurring due toinfluence of a non-uniform distribution of refractive indexes inside ofthe optical scanning lens;

FIG. 5 illustrates a method of measuring a distribution of refractiveindexes inside of a lens;

FIG. 6 illustrates a distribution of refractive indexes of an opticalscanning lens in a first embodiment of the present invention;

FIG. 7 illustrates a distribution of refractive indexes of an opticalscanning lens in a second embodiment of the present invention;

FIG. 8 illustrates a distribution of refractive indexes of an opticalscanning lens in a third embodiment of the present invention;

FIG. 9 illustrates a distribution of refractive indexes of an opticalscanning lens in a fourth embodiment of the present invention; and

FIG. 10 illustrates an image forming apparatus in one embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates an optical scanning device in one embodiment of thepresent invention.

A divergent beam emitted from a semiconductor laser 10 (light source) istransformed into a form, such as a parallel beam, suitable for asubsequent optical system by a coupling lens 12, passes through anopening of an aperture 14 so as to undergo beam shaping thereby, iscondensed by a cylindrical lens 16 along sub-scanning directions whilebeing reflected by a mirror 18, and thus is imaged to be a line imagelong along main scanning directions on or in the vicinity of adeflection reflective surface of a polygon mirror 20 (light deflector).

The beam reflected by the deflection reflective surface of the polygonmirror 20 is deflected thereby at a uniform angular velocity withuniform-velocity rotation of the polygon mirror 20, while being incidenton an optical scanning lens 30 (forming a scanning and imaging opticalsystem), is condensed onto or to the vicinity of a surface to be scanned40 (substantially, a photosensitive surface of a photoconductivephotosensitive body) by a function of the lens 30, and, thus, the beamforms a beam spot on the surface to be scanned 40. By this beam spot,the surface to be scanned 40 is scanned in the main scanning direction.The photosensitive surface of the surface to be scanned 40 is moved inthe sub-scanning direction (perpendicular to FIG. 1) and,simultaneously, the above-mentioned optical scanning along the mainscanning direction is repeated. Thereby, writing of a latent image isperformed onto the surface to be scanned 40. The above-mentioned opticalscanning by the beam spot is made to be at a uniform velocity due to thecharacteristics/performance of rendering the uniform velocity of thescanning and imaging optical system 30.

In this configuration, the optical scanning lens 30 itself forms thescanning and imaging optical system. When the scanning and imagingoptical system includes a plurality of optical components (a pluralityof lenses, a combination of a lens and a concave mirror, or the like),it is possible that the scanning and imaging optical system includes oneor a plurality of the optical scanning lens(es) according to the presentinvention described below.

The optical scanning lens 30 is formed through plastic mold (molding byusing a plastic material).

The optical scanning lens 30 has a distribution of refractive indexes ina region thereof through which the beam passes (with regard to the mainscanning direction, a region corresponding to an effective writing rangeW on the surface to be scanned 40, shown in FIG. 1).

The distribution of refractive indexes will now be described withreference FIGS. 2A, 2B, 2C, 2D and 2E.

In FIGS. 2A through 2E, a lens 1 corresponding to the above-mentionedoptical scanning lens 30 formed through plastic mold is shown. However,as FIGS. 2A through 2E are drawings merely for illustrating a concept ofthe distribution of refractive indexes, and the distribution ofrefractive indexes shown in FIGS. 2A through 2E is different from thatof the optical scanning lens 30 according to the present invention.

FIG. 2A illustrates the distribution of refractive indexes along animaginary section of the lens 1 taken along the above-described mainscanning section, by contour lines. In this figure, the nearer to thecenter the position inside of the lens becomes, the lower the refractiveindex at the position becomes.

FIG. 2C illustrates the distribution of refractive indexes along animaginary section of the lens 1 taken along the sub-scanning sectionincluding the optical axis, by contour lines. Also in this figure, thenearer to the center the position inside of the lens becomes, the lowerthe refractive index at the position becomes.

As shown in FIG. 2C, an x-direction and a y-direction are set, and,also, a z-direction is set as a direction perpendicular to FIG. 2C. They-direction corresponds to the optical-axis direction, x-directioncorresponds to the sub-scanning direction. Accordingly, the z-directioncorresponds to the main scanning direction.

An absolute refractive index at each position (x, y) in the sub-scanningsection at an arbitrary position z along the main scanning direction isrepresented by n(x, y).

An average of the absolute refractive indexes n(x, y) along the y-axisdirection for each x coordinate position is defined by the followingoperation:[∫n(x, y)dy]/d(x)where d(x) denotes a lens thickness at each x coordinate. The aboveintegration is performed throughout the thickness d(x).

An appropriate reference value is set for the result of theabove-mentioned operation. Then, a difference between the thus-setreference value and the above-mentioned operation result is obtained.Thereby, a one-dimensional relative y-axis-averaged refractive indexesΔn(x) along the x-axis direction is obtained from averaging, along they-axis direction, two-dimensional absolute refractive indexes in an x-ysection parallel to the optical axis and sub-scanning direction.

FIG. 2E illustrates these relative refractive indexes Δn(x) with respectto the x coordinate position.

FIG. 2B illustrates relative y-axis-averaged refractive indexes alongthe z-axis direction similar to the above-mentioned relativey-axis-averaged refractive indexes along the x-axis direction, butobtained from an operation [∫n(y, z)dy]/d(z) where d(z) denotes the lensthickness at each z coordinate.

FIG. 2D illustrates relative x-axis-averaged refractive indexes alongthe y-axis direction similar to the above-mentioned relativey-axis-averaged refractive indexes along the x-axis direction, butobtained from an operation [∫n(x, y)dx]/d(y), where d(y) denotes thelens thickness at each y coordinate.

As shown in FIG. 2E, the distribution of the refractive indexes Δn(x) ofthe lens 1 shown in FIG. 2A through 2E has no located local maximum. Inthis point, this lens 1 is different from the optical scanning lensaccording to the present invention.

As described above, the relative y-axis-averaged refractive indexes areexpressed by a function with respect to the coordinate variable x alongthe sub-scanning direction, and, in general, can be expressed by apolynominal of x, below:A+Bx+Cx²+Dx³+Ex⁴+ . . .In general, in many cases, the optical scanning lens has a shapesymmetrical with respect to the optical axis along the sub-scanningdirections, and, thus, the distribution of the refractive indexes issymmetrical with respect to the optical axis along the sub-scanningdirections. Accordingly, the distribution of the refractive indexes canbe practically expressed by the following polynominal of even order fromamong 4-th order through 10-th order:a+bx²+cx⁴+dx⁶+ex⁸+fx¹⁰

Then, influence of the above-mentioned distribution of the relativey-axis-averaged refractive indexes Δn(x) to opticalperformance/characteristics of the optical scanning lens will now bedescribed.

For this purpose, the distribution of the relative y-axis-averagedrefractive indexes Δn(x) is expressed by the following quadraticapproximation:Δn(x)=n ₀ +n ₁ ·x+Δn·x ²+δ(x)In this equation, δ(x) denotes a residual of the above-mentionedapproximation. In each term of the right side of the equation, asecondary coefficient Δn gives a large influence to the opticalperformance. It is possible to omit the primary coefficient n₁ accordingto the above-mentioned standpoint of symmetry. As a result, theabove-mentioned equation can be expressed as follows:Δn(x)≈n₀+Δn·x²

Thereby, it is possible to calculate the secondary coefficient Δn.

In the above-mentioned equation, the secondary coefficient Δn functionsas a lens power.

The influence of the secondary coefficient Δn to the lens function willnow be described with reference FIG. 3.

In FIG. 3, LN denotes a lens, E, F denote front and rear principalpoints thereof, respectively, P denotes an object point, and Q denote animage point. ‘f’ denotes a focal length according to design of the lensLN (that is, the focal length assuming that the distribution ofrefractive indexes inside of the lens LN is uniform), S, S′ denote anobject length and an image length according to the design.

As mentioned above, it can be assumed that the distribution ofrefractive indexes has a function of a lens. Accordingly, it is possibleto assume a lens equivalent to the distribution of refractive indexes.

As shown in FIG. 1, L denotes a distance (conjugate length) between thedeflection reflective surface of the light deflector 20 and the surfaceto be scanned 40. Further, a lateral magnification of the scanning lens30 is represented by β, Δn denotes the secondary coefficient of theabove-mentioned Δn(x), and the thickness of the lens is represented byt, and, then, a defocus amount ΔS′ (see FIG. 3) can be expressed by thefollowing expression through approximation:ΔS′≈{β/(β−1)·L}²·(2Δn·t)Thus, the defocus amount ΔS′ is approximately in proportion to Δn.

When the optical scanning lens 30 has a positive power, in a case wherethe refractive index at the lens periphery is higher than that of thelens center as mentioned above, the distribution of refractive indexesfunctions equivalently as a concave lens, and, thereby, functions toshift a position, at which the beam spot to be condensed onto thesurface to be scanned is actually condensed, in a direction such as tobe far away from the light deflector 20, from a position according tothe design.

In FIG. 4, a vertical axis represents a cross-sectional diameter of abeam, and a horizontal axis represents a position along the beam(difference from the surface to be scanned). The vertical axis coincideswith the position of the photosensitive surface as the surface to bescanned.

When the distribution of refractive indexes is uniform inside of theoptical scanning lens, the relationship between the position along thebeam and diameter of the beam is, as indicated by a broken curve, shownin FIG. 4, such that the diameter of the beam becomes minimum at theposition of the surface to be scanned (actually, the photosensitivesurface; thus, the defocus amount is zero). However, when thedistribution of refractive indexes is not uniform inside of the lens,the relationship between the position along the beam and diameter of thebeam is, as indicated by a solid curve, such that the diameter of thebeam at the position of the surface to be scanned (actually, thephotosensitive surface) is larger than the value according to the design(crossing point between the broken curve and vertical axis), due toso-called ‘beam thickening’ occurring due to the defocus.

As the defocus amount ΔS′ is approximately proportional to the secondarycoefficient An as mentioned above, it is possible to reduce the defocusamount ΔS′ by reducing the secondary coefficient Δn.

The above-mentioned equation:Δn(x)≈n₀+Δn·x²represents a parabola. Accordingly, the smaller the An becomes, thesmaller the variation rate of the refractive index with respect to thevariable x. In other words, as the distribution of refractive indexesinside of the lens becomes nearer to a uniform one, the defocus amountresulting therefrom becomes smaller. This fact is reasonable.

Before further proceeding with the description, how to measure thedistribution of relative y-axis-averaged refractive indexes Δn(x) willnow be described. The following method is one proposed by the presentinventor and so forth (see Japanese Laid-open Patent Application No.11-044641).

FIG. 5 illustrates an apparatus of measuring a refractive-indexdistribution using a Mach-Zehnder interferometer as a basic arrangementthereof.

A laser beam which is coherent light is emitted by a laser light source1A, is transformed into a parallel beam as a result of a diameterthereof being enlarged by a beam expander 3, and is incident on a beamsplitter 5. The beam splitter 5 splits the incident laser beam into twobeams. Specifically, the incident laser beam is split by the beamsplitter 5 into one laser beam which is obtained as a result of beingbent at a right angle by the beam splitter 5 and is of a reference wave‘a’, and another laser beam which is obtained as a result of beingtransmitted straightly by the beam splitter 5, being reflected by areflective mirror 9 and being transmitted by a phase object as an objectto be examined A and is of a wave to be examined ‘b’. The beam splitter5 splits the incident beam in a manner such that a ratio of intensitiesof the reference wave ‘a’ and wave to be examined ‘b’ be approximately‘1:1’.

A reflective mirror 7 is supported by an electricity-movement convertingdevice 19 formed of a piezoelectric device or the like, and is arrangedin a manner such that a length of light path of the reference wave ‘a’can be changed on the order of wave length for a purpose of performinganalysis of interference fringes in accordance with a phase shiftingmethod.

The reference wave ‘a’ is reflected by the reflective mirror 7 andreaches a beam splitter 11. The wave to be examined ‘b’ is reflected bythe reflective mirror 9, is transmitted by the object to be examined A,and reaches the beam splitter 11. The beam splitter 11 joins thereference wave ‘a’ and wave to be examined ‘b’ together into a joinedbeam (a+b), and splits the joined beam into two beams. Theelectricity-movement converting device 19 is adjusted so that ‘a phasedifference of mπ/2’ be obtained in length of light path between thereference wave ‘a’ and wave to be examined ‘b’ to be joined together,where ‘m’ is an integer. One split beam of the joined beam split by thebeam splitter 11 is incident on an imaging lens 13, and, thereby, animage of interference fringes (of the reference wave ‘a’ and wave to beexamined ‘b’) is formed on an image pickup surface of aninterference-fringe detector 15. As the interference-fringe detector 15,a linear CCD, or an array-like sensor, disposed perpendicularly to theinterference fringes is used. The other split beam of the joined beamsplit by the beam splitter 11 is incident on an image pickup surface ofa CCD camera for monitoring 23, and, thereby, an image of theinterference fringes is formed thereon, through an imaging lens 31.

A refractive index of the object to be examined A is considerablydifferent from that of the air, and, unless an incident side and anemitting side of the object to be examined A are parallel to oneanother, the wave to be examined ‘b’ transmitted by the object to beexamined A converges/diverges irregularly depending on a shape of theobject to be examined A. In order to cause an image of interferencefringes to be formed on the image pickup surface of theinterference-fringe detector 15, the wave to be examined ‘b’ should be‘an approximately parallel beam’. The following arrangement is made inorder to cause the wave to be examined ‘b’ having been transmitted bythe object to be examined A to be an approximately parallel beamregardless of a shape of the object to be examined A.

That is, the object to be examined A is set inside a cell 21 provided ona light path of the wave to be examined ‘b’, and the cell 21 is filledwith a test liquid B ‘made up so that a refractive index thereof isapproximately equal to a refractive index of the object to be examinedA’. Two ends of the cell 21, that is an incident window 25 and anemitting window 27 for the wave to be examined ‘b’, are parallel to oneanother, and optical flats 28 and 29 each having a high surface accuracyare attached thereto, and the cell 21 is sealed for preventing theliquid inside thereof from leaking.

The cell 21 filled with the object to be examined A and test liquid B isan object, a distribution of refractive indexes of which is uniformthrough the entirety thereof, and an incident surface and an emittingsurface of which are parallel to one another. Accordingly, the wave tobe examined ‘b’ transmitted by the cell 21 is emitted therefrom as beingan approximately parallel beam. When a refractive-index distributioninside the object to be examined A is non-uniform, a wave surface of thewave to be examined ‘b’ emitted from the cell 21 has ‘a curved-surfaceshape depending on the refractive-index distribution’. Interferencefringes, an image of which is formed on the image pickup surface of theinterference-fringe detector 15, develop due to interference between thewave to be examined ‘b’ of the above-mentioned curved-surface shape andthe reference wave ‘a’ which is a plane wave. Then the curved-surfaceshape of the wave to be examined ‘b’ can be measured by well-knownanalysis of these interference fringes.

The image of the interference fringes is detected by theinterference-fringe detector 15, undergoes photoelectric conversion soas to become an electric image signal, is converted into a digitalsignal by an A-D converter 33, and is input to a calculation device 17.

The calculation device 17 includes a transmitted wave surface measuringunit 35 which measures and calculates a transmitted wave surface (ashape of wave surface of the wave to be examined ‘b’) by analysis of theinterference fringes. Specifically, the calculation device 17 is apersonal computer or the like which ‘has a CPU and performs variouscalculation processes in accordance with programs stored in a hard diskdrive or the like thereof’.

A refractive-index distribution of the optical scanning lens as theobject to be examined A is measured as follows:

It is preferable that the design values for the outline shape andrefractive index of the optical scanning lens are known. In measurementof the distribution of refractive indexes, data of the outline shapeneeded is the thickness along the optical axis. However, the measurementresult is obtained as an amount reverse proportional to the thickness.Accordingly, even when an error is included in the thickness data given,it results in merely a little influence thereof to the result. Withregard to the deign data of refractive index, the data is used forselecting the optimum test liquid B having a refractive indexapproximately the same as that of the object to be examined. Also inthis case, merely a little influence to the measurement resultstherefrom as a measurement error.

The optical scanning lens as the object to be measured A is set in thecell 21, the coherent light from the laser light source 1 is incident onthe optical scanning lens, and, as described above, an image ofinterference fringes is formed on the interference-fringe detector 15.An image signal of the image of the interference fringes output by theinterference-fringe detector 15 is input to the calculation device 17,the transmitted wave surface measuring unit 35 in the calculating device17 performs ‘analysis of the interference fringes’, and, thus, atransmitted wave surface WF(x) is measured. The apparatus shown in FIG.5 is arranged so that the longitudinal direction of the linear CCD ofthe interference-fringe detector 15 corresponds to the x direction(sub-scanning direction) described above with respect to the opticalscanning lens.

The thickness d(x) in the optical-axis direction of the optical scanninglens as the object to be examined A is obtained previously from thedesign data of the optical scanning lens, as mentioned above, ormeasured data thereof by a general-purpose measuring apparatus.

As mentioned above, based on the output of the linear CCD of theinference-fringe detector 15, the transmitted wave surface WF(x) ismeasured by the transmitted wave surface measuring unit 35. Then, anarbitrary position on the linear CCD is determined to be a position of‘x=0’ and a reference transmitted wave surface WF(0) is obtained, and,then, Δn(x) is calculated by the following equation:Δn(x)={WF(x)−WF(0)}·λ/d(x)

Thus, the distribution of the refractive indexes Δn(x) can be calculatedfor an arbitrary measurement section. A change of the measurementsection can be performed by changing a position relationship between thelinear CCD and the lens to be examined so that the lens to be examinedis moved in the z direction relative to the linear CCD.

In the above-described method, Δn(x) is calculated from ‘anoptical-axis-directional-thickness-directionally added-up transmittedwave surface’. Accordingly, although ‘a refractive-index distribution ofoptical-axis direction’ such as that shown in FIG. 2D cannot beobtained, the average data Δn(x) obtained as a result of adding up alongthe optical-axis direction is sufficient to grasp the opticalcharacteristics of the optical scanning lens. Further, because Δn(x) isof one dimension, this can be easily managed as an evaluation itemadvantageously. Further, Δn(x) in the above equation is a function ofonly ‘x’. However, it is possible to perform two-dimensional measurementusing (x, z) as variables.

Δn(x) thus calculated as mentioned above can be practically expressed bythe following polynomial, as mentioned above:a+bx²+cx⁴+dx⁶+ex⁸+fx¹⁰

Then, each coefficient a, b, c, d, e and f of the above-mentionedpolynomial may be obtained through least squire or the like. Thereby, itis possible to immediately obtain the relative y-axis-averagedrefractive indexes Δn(x) at a coordinate position x along the x-axis.

By such a measuring method as that described above, it is possible tomeasure, in a non-destructive manner, the distribution of the relativey-axis-averaged refractive indexes Δn(x) inside of the optical scanninglens formed through plastic mold.

Through such a measurement work, the present inventor found out that thedistribution of the relative y-axis-averaged refractive indexes Δn(x) ofthe optical scanning lens varies according to a manufacturing conditionof the optical scanning lens, especially, according to a condition inwhich a heated resin injected into a die and thus molded is cooled.

When the die is left in a chamber of a normal temperature after themolding, and thus, natural cooling is performed thereon, one or severalminutes are required for cooling it until the optical scanning lens inthe die can be removed from the die. In this case, as the requiredcooling time is short, manufacturing efficiency is satisfactory.However, in such a manner, a distribution of the refractive indexes likea parabola such as that shown in FIGS. 2A through 2E develops.

In contrast thereto, when the optical scanning lens is removed from thedie (or left in the die) after the molding, then, is brought into athermostatic chamber, and is cooled gradually/slowly for ten and somehours, it is possible to reduce such a non-uniform distribution ofrefractive indexes developing inside of the optical scanning lens,remarkably. However, by such a manner, manufacturing efficiency is veryunsatisfactory as a long time is required for the cooling.

When the optical scanning lens is removed from the die (or left in thedie) after the molding, is brought into a thermostatic chamber, and iscooled gradually/slowly but for the order of 10 through 60 minutes as aresult of the room temperature being gradually lowered, a local maximumappears in the distribution of refractive indexes inside of the lens asin the present invention.

A feature of the present invention is that the distribution (curve) ofthe relative y-axis-averaged refractive indexes Δn(x) inside of theoptical scanning lens has such a local maximum.

In general, the distribution of refractive indexes corresponds to aquadratic curve such that the refractive index becomes smaller as theposition becomes near to the center, as described above with referenceFIGS. 2A through 2E. Accordingly, increase in the amount of thesecondary coefficient An directly results in increase in the defocusamount. It is possible to reduce the defocus amount by reducing thedifference [max{Δn(x)}−min{Δn(x)}] between the maximum value max{Δn(x)}and the minimum value min{Δn(x)} of the distribution of the relativey-axis-averaged refractive indexes Δn(x). However, in order to satisfythis requirement, a considerably long time is required to cool themolded plastic material, as mentioned above. Thereby, the productivityis degraded.

In contrast thereto, when the distribution (curve) of the relativey-axis-averaged refractive indexes Δn(x) has a local maximum as in theoptical scanning lens according to the present invention, it is possibleeffectively to reduce the secondary coefficient An which has a largeinfluence onto the optical performance as the defocus amount, even whenthe above-mentioned difference [max{Δn(x)}−min{Δn(x)}] itself is large.

Each of the optical scanning lenses in first through fourth embodimentsof the present invention which will be described now is assumed to beused as the optical scanning lens 30 of the optical scanning devicedescribed above with reference to FIG. 1.

The first through third embodiments thereof are produced throughsimulations of typical distributions (curves) of the relativey-axis-averaged refractive indexes Δn(x) each having a local maximum.

The optical scanning lens in the first embodiment will now be described.

FIG. 6 illustrates the distribution of the relative y-axis-averagedrefractive indexes Δn(x) of the optical scanning lens in the firstembodiment of the present invention (simulation result).

A vertical axis of FIG. 6 represents the relative y-axis-averagedrefractive index Δn(x). A horizontal axis thereof represents a positionof the optical scanning lens along a short-length direction thereof,that is, the sub-scanning direction (x-axis direction) mentioned above.The distribution of the relative y-axis-averaged refractive indexesΔn(x) shown in FIG. 6 is one on a sub-scanning section including theoptical axis of the optical scanning lens. Accordingly, the origin ofthe horizontal axis coincides with the optical axis. A scale of thehorizontal axis is expressed as a result of the effective diameter(range through which the proper beam passes through the lens) along thesub-scanning direction being normalized into a range between ±1. As anactual length, the order of ±2 mm (corresponding to ±1 in the scale ofthe horizontal axis shown in the figure) is assumed.

A curve 6-1 in FIG. 6 represents the above-mentioned distribution of therelative y-axis-averaged refractive indexes Δn(x) of the opticalscanning lens in the first embodiment of the present invention. Thecurve 6-1 has a local maximum LMAX[Δn(x)]=0.16×10⁻⁵. Further, the curve6-1 has local minimums 0 in the vicinity of ±0.6 of the horizontal axis.These local minimums are also the minimum values min[Δn(x)]. The maximumvalue max[Δn(x)] of Δn(x) is 0.71×10⁻⁵ at ±1 of the horizontal axis.

A curve 6-2 in FIG. 6 is obtained from approximation of theabove-mentioned curve 6-1 by the above-mentioned quadratic expression:Δn(x)≈n₀+Δn·x²In this case, the secondary coefficient Δn is 0.1.

A curve 6-0 shown in FIG. 6 is a curve representing the distribution ofthe relative y-axis-averaged refractive indexes Δn(x) required by therequired optical performance of the optical scanning lens in the firstembodiment. That is, first, the secondary coefficient An correspondingto the allowable defocus amount under the circumstances in which theoptical scanning lens in the first embodiment is actually used isobtained, and, by using the thus-obtained Δn, Δn(x)≈n₀+Δn·x² isdetermined, and, is represented by the curve 6-0. In this case, n₀=0,and Δn=0.1. This curve 6-0 representing the distribution of the relativey-axis-averaged refractive indexes Δn(x) according to the requiredoptical performance of the optical scanning lens in the first embodimentmay vary according to the optical requirement. The optical requirementapplied in this case is such that the maximum value of the distributionof the relative y-axis-averaged refractive indexes Δn(x) is such thatmax[Δn(x)]=0.4×10⁻⁵.

As can be seen from a comparison between the curves 6-0 and 6-2,although the optical scanning lens in the first embodiment actually hasthe largely non-uniform distribution of the refractive indexes (that is,0.71×10⁻⁵) shown by the curve 6-1, the curve 6-2 which actuallydetermines the optical characteristic (defocus) is substantially thesame as the curve 6-0 representing the distribution of the refractiveindexes required by the required optical performance of the opticalscanning lens. Accordingly, even having the remarkably non-uniformdistribution of the refractive indexes, the optical scanning lens in thefirst embodiment has the necessary/proper optical characteristic asbeing used as the optical scanning lens.

With regard to the maximum value and minimum value of the distributionof the relative y-axis-averaged refractive indexes Δn(x), even a moldproduct having a difference between the maximum value and minimum value1.8 times (0.71/0.4) that of the lens according to the requirement ofthe curve 6-0 in optical characteristic has a defocus amount equivalentto the lens according to the requirement of the curve 6-0. In otherwords, an allowable range of the difference between the maximum valueand minimum value of Δn(x) can be widened 1.8 times in this embodiment.

In the above-described first embodiment of the present invention, valuesof the above-mentioned requirements (1) and (2) are as follows:LMAX[Δn(x)]−min[Δn(x)]=0.16×10⁻⁵{max[Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]}=4.4

The optical scanning lens in the second embodiment of the presentinvention will now be described with reference FIG. 7.

FIG. 7 illustrates the distribution of the relative y-axis-averagedrefractive indexes Δn(x) (simulation result) of the optical scanninglens in the second embodiment of the present invention. FIG. 7 is drawnin a manner the same as that in which FIG. 6 is drawn. Accordingly,curves 7-1, 7-2 and 7-0 correspond to the curves 6-1, 6-2 and 6-0,respectively.

Also in the second embodiment illustrated in FIG. 7, the secondarycoefficient Δn with regard to the curves 7-2 and 7-0 has a value of 0.1.Values of the above-mentioned requirements (1) and (2) are as follows:LMAX[Δn(x)]−min[Δn(x)]=2.2×10⁻⁵{max [Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]}=0.66Thus, the curve 7-1 has a high local maximum, and a ratio in differencebetween the maximum value and minimum value of the distribution of therelative y-axis-averaged refractive indexes Δn(x) is 8.4 (3.4/0.4).Accordingly, an allowable range of the difference between the maximumvalue and minimum value of Δn(x) can be widened 8.4 times in comparisonto the lens to satisfy the curve 7-0 with regard to the opticalcharacteristic.

The optical scanning lens in the third embodiment of the presentinvention will now be described with reference FIG. 8.

FIG. 8 illustrates the distribution of the relative y-axis-averagedrefractive indexes Δn(x) (simulation result) of the optical scanninglens in the third embodiment of the present invention. FIG. 8 is drawnin a manner the same as that in which FIG. 6 is drawn. Accordingly,curves 8-1, 8-2 and 8-0 correspond to the curves 6-1, 6-2 and 6-0,respectively.

In the third embodiment illustrated in FIG. 8, the secondary coefficientΔn with regard to the curves 8-2 and 8-0 has a value of 3.0. Values ofthe above-mentioned requirements (1) and (2) are as follows:LMAX[Δn(x)]−min[Δn(x)]=1.0×10⁻⁵{max[Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]}=14.5A ratio in difference between the maximum value and minimum value of thedistribution of the relative y-axis-averaged refractive indexes Δn(x) is1.2 (14.5/12). Accordingly, an allowable range of the difference betweenthe maximum value and minimum value of Δn(x) can be widened by the orderof 20% in comparison to the lens to satisfy the curve 8-0 with regard tothe optical characteristic.

Taking into consideration of the above-described optical scanning lensesin the first, second and third embodiments, as shown by theabove-mentioned requirement (1), it is preferable to satisfy thefollowing requirement:0.1×10⁻⁵ <LMAX[Δn(x)]−min [Δn(x)]<4×10⁻⁵with respect to difficulty in design and working for the opticalscanning lens.

When this value is less than the lower limit 0.1×10⁻⁵, the local maximumbecomes smaller. Accordingly, the effect of reducing the defocus amountis small, and, a measurement error cannot be ignored.

When the value is higher than the upper limit 4×10⁻⁵, working for thelens becomes difficult and thus requires high costs. Also, the wavefrontaberration becomes approximately 0.3λ even in a lens having a thicknessof 5 mm, for example. Accordingly, there is a possibility that beamthickening occurs due to the wavefront aberration.

In the above-mentioned optical scanning lens in the second embodiment,the range of the effective diameter is ±1 in relative value. However,when the range of the effective diameter is made to be ±0.8 in FIG. 7,the secondary coefficient An is approximately zero substantially, even anon-uniform distribution of the refractive indexes present inside of thelens, defocus hardly occurs, and, thus, it is further preferable. Inthis case,{max[Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]}≈1Accordingly, a preferable range of the parameter{max[Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]} is as follows as in theabove-mentioned requirement (2):1≦{max[Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]}<15When this value exceeds the upper limit 15 (similarly to the thirdembodiment shown in FIG. 8), the effective of reducing the defocusamount obtained as a result of the distribution of the refractiveindexes having the local maximum hardly appears.

Further, when the range of the effective diameter is reduced to ±0.5, nopart including the local minimum is included in the range. In this case,a defocus amount develops slightly in the reverse direction. However, noproblem occurs with respect to the performance, when the followingrequirement (1) is satisfied:0.1×10⁻⁵ <LMAX[Δn(x)]−min[Δn(x)]<4×10⁻⁵

However, the effect of reducing the defocus amount is larger in a casewhere both the local maximum and local minimum are present in thedistribution of the refractive indexes Δn(x).

The distribution of the refractive indexes developing inside of a lensdepends on a rate of cooling of a molded plastic material as mentionedabove. As can be seen from FIGS. 2A through 2E, the optical scanninglens has a rectangular shape long along the main scanning direction, ingeneral. Further, in general, in the optical scanning lens, thethickness thereof decreases as the position becomes far away from theoptical axis thereof along the main scanning direction, as shown in FIG.2A. The width thereof along the sub-scanning direction (x-axisdirection) is fixed with respect to the position along the main scanningdirection.

In other words, not in the main scanning direction but in thesub-scanning direction and also in the thickness direction, heat easilymoves when the molded plastic is cooled.

Accordingly, tendency of non-uniform distribution of the refractiveindexes is relatively small along the main scanning direction as shownin FIG. 2B. Further, in consideration of reduction in lens thickness inthe main-scanning-directional periphery of the lens in general, it canbe considered that the above-mentioned secondary coefficient Δnresulting in defocus decreases as the position becomes far away from theoptical axis of the lens along the main scanning direction.

Accordingly, it is not necessary that the optical scanning lenssatisfies the above-mentioned requirements in that the distribution(curve) of the relative y-axis-averaged refractive indexes Δn(x) has alocal maximum or both a local maximum and a local minimum; and theabove-mentioned requirements (1) and/or (2) are satisfied, throughoutthe entire range of the effective diameter (range through which theproper beam passes through the lens) along the main scanning direction.

That is, it is possible to obtain a practically sufficient opticalperformance only as a result of the optical scanning lens satisfying therequirement in that the distribution of the relative y-axis-averagedrefractive indexes Δn(x) has a local maximum or both a local maximum anda local minimum; and the above-mentioned requirements (1) and/or (2) aresatisfied, through a main-scanning-directional range in the vicinity ofthe optical axis (for example, a range of 2 through 5 mm from theoptical axis in each of both directions along the main scanningdirection). Further, in consideration of variation of the relativey-axis-averaged refractive index Δn(x) along the main scanning directionbeing continues and gentle, it can be said that, when the opticalscanning lens satisfies the requirement in that, only in a sub-scanningsection of the lens on or in the vicinity of the center thereof alongthe main scanning direction in a range of the lens through which theproper beam passes therethrough, the distribution of the relativey-axis-averaged refractive indexes Δn(x) has a local maximum or both alocal maximum and a local minimum; and the above-mentioned requirements(1) and/or (2) are satisfied, this optical scanning lens can be usedwhile no problem occurs with regard to the defocus characteristic.

When an inspection for determining whether or not a lens formed throughplastic mold is suitable as the optical scanning lens can be made onlyby using one sub-scanning section on or in the vicinity of themain-scanning-directional center of the lens as mentioned above, it ispossible to effectively improve the efficiency of inspection especiallyduring a mass-producing process of the optical scanning lens.

Each of the above-mentioned curves 6-1, 7-1 and 8-1 shown in FIGS. 6, 7and 8 with respect to the above-described first, second and thirdembodiments, respectively, represents the distribution of the relativey-axis-averaged refractive indexes Δn(x) for the sub-scanning sectionincluding the optical axis thereof.

The optical scanning lens in the fourth embodiment of the presentinvention will now be described with reference FIG. 9.

FIG. 9 illustrates the distribution of the relative y-axis-averagedrefractive indexes Δn(x) (simulation result) of the optical scanninglens in the fourth embodiment of the present invention. FIG. 9 is drawnin a manner the same as that in which FIG. 6 is drawn with respect tothe first embodiment.

A curve 9A shown in FIG. 9 represents actually measured values of thedistribution of the relative y-axis-averaged refractive indexes Δn(x)for the sub-scanning section including the optical axis of the opticalscanning lens in the fourth embodiment. A curve 9-1 of chain lineshowing in FIG. 9 is obtained as a result of these actually measuredvalues being expressed by using the above-mentioned polynomial:a+bx²+cx⁴+dx⁶+ex⁸+fx¹⁰and corresponds to the curve 6-1 shown in FIG. 6.

According to the curve 9-1, LMAX[Δn(x)]=0.215×10⁻⁵,min[Δn(x)]=0.03×10⁻⁵, and max[Δn(x)]=0.69×10⁻⁵. Accordingly, the valuesof the above-mentioned requirements (1) and (2) are as follows:LMAX[Δn(x)]−min[Δn(x)]=0.19×10⁻⁵{max[Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]}=3.47

A curve 9-2 is obtained as a result of the curve 9-1 being approximatedby using the quadratic formula:Δn(x)≈n₀+Δn·x²and, at this time, the secondary coefficient Δn=0.1.

A material of the optical scanning lens in the fourth embodiment ispolyolefin resin. After molding this material, the optical scanning lensremoved from the die is brought into a thermostatic chamber, and iscooled gradually for approximately one hour. The fourth embodiment hasthe distribution of the relative y-axis-averaged refractive indexesΔn(x) near to that of the first embodiment produced in simulation, andthus, has functions similar to those of the first embodiment.

It is assumed that each of the above-described first through thirdembodiments produced in simulation is made of polyolefin by using thedie used for producing the fourth embodiment.

As mentioned above, each of the optical scanning lenses in the firstthrough fourth embodiments described with reference to FIGS. 6 through 9is the optical scanning lens 30 used as the scanning and imaging opticalsystem which condenses the beam deflected by the light deflector 20 onor in the vicinity of the surface to be scanned 40, is formed throughplastic mold, and such that a distribution of the relativey-axis-averaged refractive indexes Δn(x) inside of the lens within arange through which the beam passes through the lens has a localmaximum.

Further, the above-mentioned distribution of the relativey-axis-averaged refractive indexes Δn(x) has also a local minimum, and,also, the following requirement is satisfied:0.1×10⁻⁵ <LMAX[Δn(x)]−min[Δn(x)]<4×10⁻⁵  (1)where LMAX[Δn(x)] denotes the above-mentioned local maximum, andmin[Δn(x)] denotes the minimum value of the above-mentioned distributionof the refractive indexes Δn(x), and, also, the following requirement issatisfied:1≦{max[Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]}<15  (2)where max[Δn(x)] denotes the maximum value of the above-mentioneddistribution of the refractive indexes Δn(x).

Further, within the range through which the beam passes through thelens, and also, in a sub-scanning section on or in the vicinity of thecenter of the lens along the main scanning direction, the distributionof the refractive indexes Δn(x) inside of the lens has the local maximumand the local minimum, and, also, the following requirements aresatisfied:0.1×10⁻⁵ <LMAX[Δn(x)]−min[Δn(x)]<4×10⁻⁵  (1)where LMAX[Δn(x)] denotes the above-mentioned local maximum, andmin[Δn(x)] denotes the minimum value of the above-mentioned distributionof the refractive indexes Δn(x), and, also, the following requirement issatisfied:1≦{max[Δn(x)]−min[Δn(x)]}/{LMAX[Δn(x)]−min[Δn(x)]}<15  (2)where max[Δn(x)] denotes the maximum value of the above-mentioneddistribution of the refractive indexes Δn(x).

Further, in the optical scanning device employing any one of theabove-mentioned optical scanning lenses in the first through fourthembodiments of the present invention as the optical scanning lens 30,the beam coming from the light source 10 is deflected at a uniformangular velocity by the light deflector 20 having the deflectionreflective surface, the deflected beam is condensed onto the surface tobe scanned 40 by the scanning and imaging optical system 30, and, thus,optical scanning of the surface to be scanned 40 in a uniform velocityis performed. In this configuration, the optical scanning lens in one ofthe first through fourth embodiments of the present invention is used atleast a part of the above-mentioned scanning and imaging optical system.Actually, in the configuration shown in FIG. 1, the optical scanninglens 30 itself forms the scanning and imaging optical system.

The optical scanning device according to the present invention may alsobe embodied as a so-called multi-beam scanning device.

With reference to FIG. 10, an image forming apparatus in one embodimentof the present invention will now be described.

The image forming apparatus shown in FIG. 10 is a laser printer, forexample.

This laser printer 100 has a cylindrical photoconductive photosensitivebody acting as a photosensitive medium 111. Around the photosensitivemedium 111, a charging roller 112 acting as a charging unit, adeveloping device 113, a transfer roller 114, and a cleaning device 115are disposed. It is also possible to use a well-known corona charger asthe charging unit.

Further, an optical scanning device 117 using a laser beam LB isprovided, and performs exposure of the photosensitive medium 111 throughoptical writing between the charging roller 112 and developing device113.

As shown in FIG. 10, a fixing device 116, a cassette 118, a pair ofregistration rollers 119, a paper feeding roller 120, a conveying path121, a pair of paper ejecting rollers 122, and a tray 123 are alsoprovided. Transfer paper P is used as a sheet-type recording medium.

When image formation is performed, the photosensitive medium 111 isrotated clockwise at a uniform velocity, the surface thereof is chargeduniformly by the charging roller 112, and an electrostatic latent imageis formed on the surface (surface to be scanned) of the photosensitivemedium 1111 through exposure by optical writing with the laser beam LBof the optical scanning device 117. The thus-formed electrostatic latentimage is a so-called negative latent image having an image part exposedthereby.

This electrostatic latent image is developed inversely by the developingdevice 113, and, thus, a toner image is formed on the photosensitivemedium 111.

The cassette 118 containing the transfer paper P is detachable from/tothe body of the image forming apparatus 100. In the state in which thecassette 118 is loaded as shown in the figure, the top one sheet of thetransfer paper P is fed by the paper feeding roller 120. The thus-fedtransfer paper P is nipped by the pair of registration rollers 119 atthe top of the paper P. The pair of registration rollers 119 feed thetransfer paper P to a transfer position of the photosensitive medium 111at the time at which the toner image is moved to the transfer position.The fed transfer paper P is laid onto the toner image at the transferposition, and, by the function of the transfer roller 114, the tonerimage is transferred to the transfer paper P electrostatically.

The transfer paper P thus having had the toner image transferred theretois sent to the fixing device 116, which fixes the toner image onto thetransfer paper P. Then, the transfer paper P passes through theconveying path 121, and is ejected to the tray 123 by the pair ofejecting rollers 122. The surface of the photosensitive medium 111 isthen cleaned by the cleaning device 115, and, thus, remaining toner,paper powder and so forth are removed therefrom.

It is also possible to use an OHP sheet instead of the above-mentionedtransfer paper. A provision may be made such that the transfer of thetoner image is performed via an intermediate transfer medium such as anintermediate transfer belt or the like.

In the above-described image forming apparatus shown in FIG. 10, theoptical scanning device, shown in FIG. 1, employing the optical scanninglens such as that in any of the first, second, third and fourthembodiments of the present invention described above with reference toFIGS. 6 through 9 as the optical scanning lens/scanning and imagingoptical system thereof is used as the above-mentioned optical scanningdevice 117.

In this image forming apparatus, the photosensitive medium 111 is aphotoconductive photosensitive body, and the electrostatic latent imageformed on the photosensitive surface thereof through the uniformcharging by the charging roller 112 and the optical scanning by theoptical scanning device 117 is visualized into the toner image throughthe development by the developing device 113.

The present invention is not limited to the above-described embodiments,and variations and modifications may be made without departing from thescope of the present invention.

The present application is based on Japanese priority application No.2000-161586, filed on May 31, 2000, the entire contents of which arehereby incorporated by reference.

1. An optical scanning lens having a distribution of refractive indexinside thereof, comprising: a region within a range through which a beampasses, in which region Δn(x) decreases from a center to a periphery,wherein the Δn(x) is expressed as a variable number determinedcorresponding to a value integrated throughout a thickness d(x), thethickness d(x) is defined as a thickness of the optical scanning lens ina sub-scanning direction, and Δn(x) is a polynomial having an order ofthree or more.
 2. An optical scanning lens as claimed in claim 1,wherein the lens is formed of a plastic material.
 3. An optical scanninglens having a distribution of refractive index inside thereof,comprising: a first region and a second region within a range throughwhich a beam passes, in which Δn(x) in the first region is positive, andthe Δn(x) in the second region is negative, wherein the Δn(x) isexpressed as a variable number determined corresponding to a valueintegrated throughout a thickness d(x), the thickness d(x) is defined asa thickness of the optical scanning lens in a sub-scanning direction,and Δn(x) is a polynomial having an order of three or more.
 4. Anoptical scanning lens as claimed in claim 3, wherein the lens is formedof a plastic material.
 5. An optical scanning lens having a distributionof refractive index inside thereof, comprising: a region within a rangethrough which a beam passes, in which region Δn(x) is positive at acenter, wherein the Δn(x) is expressed as a variable number determinedcorresponding to a value integrated throughout a thickness d(x), thethickness d(x) is defined as a thickness of the optical scanning lens ina sub-scanning direction, and Δn(x) is a polynomial having an order ofthree or more.